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Gorilla robot is a new-type robot with multiple locomotion modes including biped walking, quadruped walking and brachiate locomotion. In comparison with conventional four-legged walking machines, the mechanism of the robot has particularity and complexity. In order to realize quadruped walking of the gorilla robot, we propose the gaits of forward walking, sideways walking, translational walking and turning walking, respectively. The results of simulation show that these gaits are feasible and efficient.